Problem: What do the following two equations represent? $-3x+4y = -4$ $-15x+20y = 5$
Solution: Putting the first equation in $y = mx + b$ form gives: $-3x+4y = -4$ $4y = 3x-4$ $y = \dfrac{3}{4}x - 1$ Putting the second equation in $y = mx + b$ form gives: $-15x+20y = 5$ $20y = 15x+5$ $y = \dfrac{3}{4}x + \dfrac{1}{4}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.